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Volterra kernels, Oldroyd models, and interconversion in superposition rheometry

Daniel Curtis Orcid Logo, A.R. Davies

Journal of Non-Newtonian Fluid Mechanics, Volume: 293, Start page: 104554

Swansea University Author: Daniel Curtis Orcid Logo

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DOI (Published version): 10.1016/j.jnnfm.2021.104554

Abstract

The purpose of this paper is to demonstrate how the general problem of interconversion between parallel and orthogonal superposition protocols can be treated using the kernels in a Frechet series expansion about the base viscometric flow. Such series differ from Frechet series expanded about the res...

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Published in: Journal of Non-Newtonian Fluid Mechanics
ISSN: 0377-0257
Published: Elsevier BV 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa56746
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first_indexed 2021-05-06T08:37:42Z
last_indexed 2023-01-11T14:36:10Z
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spelling 2022-07-25T12:06:19.7320801 v2 56746 2021-04-27 Volterra kernels, Oldroyd models, and interconversion in superposition rheometry e76ff28a23af2fe37099c4e9a24c1e58 0000-0002-6955-0524 Daniel Curtis Daniel Curtis true false 2021-04-27 CHEG The purpose of this paper is to demonstrate how the general problem of interconversion between parallel and orthogonal superposition protocols can be treated using the kernels in a Frechet series expansion about the base viscometric flow. Such series differ from Frechet series expanded about the rest history which are encountered in the theory of Green-Rivlin materials and the simple fluid theory of Coleman and Noll, in that nonlinear response of the material is captured at first order. Unlike first and second-order functional derivatives evaluated at the rest history, the derivatives we discuss require more than one kernel in their integral representation. However, all the kernels are inter-related. The strategy in the paper involves identifying the kernels which specify the components in the first and second order Frechet derivatives for the nonlinear constitutive models to be used in the interconversion. Interconversion between parallel and orthogonal protocols can then be effected by establishing the relationships between the kernels. Step-strain perturbations are treated by allowing differentiation in the sense of distributions. The theory is illustrated throughout by evaluating the kernels and superposition moduli associated with the incompressible corotational Maxwell and Oldroyd models. Journal Article Journal of Non-Newtonian Fluid Mechanics 293 104554 Elsevier BV 0377-0257 Superposition rheometry, Volterra kernels, Oldroyd constitutive equations, Parallel and orthogonal superposition moduli, Interconversion 1 7 2021 2021-07-01 10.1016/j.jnnfm.2021.104554 COLLEGE NANME Chemical Engineering COLLEGE CODE CHEG Swansea University EPSR , EP/N013506/1, EP/T026154/1, EP/P005985/1 ERDF EP/N013506/1, EP/T026154/1, EP/P005985/1 2022-07-25T12:06:19.7320801 2021-04-27T13:33:52.8860264 Faculty of Science and Engineering School of Engineering and Applied Sciences - Chemical Engineering Daniel Curtis 0000-0002-6955-0524 1 A.R. Davies 2 56746__19906__991fd09b945b42d5acc5c5a77ca0389d.pdf 56746.pdf 2021-05-14T16:50:31.8003327 Output 429004 application/pdf Accepted Manuscript true 2022-04-30T00:00:00.0000000 ©2021 All rights reserved. All article content, except where otherwise noted, is licensed under a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND) true eng https://creativecommons.org/licenses/by-nc-nd/4.0/
title Volterra kernels, Oldroyd models, and interconversion in superposition rheometry
spellingShingle Volterra kernels, Oldroyd models, and interconversion in superposition rheometry
Daniel Curtis
title_short Volterra kernels, Oldroyd models, and interconversion in superposition rheometry
title_full Volterra kernels, Oldroyd models, and interconversion in superposition rheometry
title_fullStr Volterra kernels, Oldroyd models, and interconversion in superposition rheometry
title_full_unstemmed Volterra kernels, Oldroyd models, and interconversion in superposition rheometry
title_sort Volterra kernels, Oldroyd models, and interconversion in superposition rheometry
author_id_str_mv e76ff28a23af2fe37099c4e9a24c1e58
author_id_fullname_str_mv e76ff28a23af2fe37099c4e9a24c1e58_***_Daniel Curtis
author Daniel Curtis
author2 Daniel Curtis
A.R. Davies
format Journal article
container_title Journal of Non-Newtonian Fluid Mechanics
container_volume 293
container_start_page 104554
publishDate 2021
institution Swansea University
issn 0377-0257
doi_str_mv 10.1016/j.jnnfm.2021.104554
publisher Elsevier BV
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Chemical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Chemical Engineering
document_store_str 1
active_str 0
description The purpose of this paper is to demonstrate how the general problem of interconversion between parallel and orthogonal superposition protocols can be treated using the kernels in a Frechet series expansion about the base viscometric flow. Such series differ from Frechet series expanded about the rest history which are encountered in the theory of Green-Rivlin materials and the simple fluid theory of Coleman and Noll, in that nonlinear response of the material is captured at first order. Unlike first and second-order functional derivatives evaluated at the rest history, the derivatives we discuss require more than one kernel in their integral representation. However, all the kernels are inter-related. The strategy in the paper involves identifying the kernels which specify the components in the first and second order Frechet derivatives for the nonlinear constitutive models to be used in the interconversion. Interconversion between parallel and orthogonal protocols can then be effected by establishing the relationships between the kernels. Step-strain perturbations are treated by allowing differentiation in the sense of distributions. The theory is illustrated throughout by evaluating the kernels and superposition moduli associated with the incompressible corotational Maxwell and Oldroyd models.
published_date 2021-07-01T04:11:56Z
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score 11.037603

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